Ultrahard nanomaterials are used extensively in cutting, milling, grinding, drilling, and other abrasive operations. Ultrahard abrasive particles currently in use include diamond, cubic boron nitride, silicon carbide (commonly known as carborundum or carbide), and silicon nitride. Of the foregoing compounds, diamond is the hardest. In fact, diamond is the hardest known material, and it is used in many modern applications such as grinding, drilling rocks, cutting concrete, polishing stones, and machining. Unfortunately, carbon's inherent reactivity with iron and silicon limit its use in some applications, such as machining steel. Therefore, a continuing and unmet need exists for alternative ultrahard particulate materials, including materials that may be used in the place of diamond.